Classical and quantum resonances for hyperbolic surfaces
Dynamical Systems
2017-08-01 v3 Differential Geometry
Spectral Theory
Abstract
For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.
Cite
@article{arxiv.1605.08801,
title = {Classical and quantum resonances for hyperbolic surfaces},
author = {Colin Guillarmou and Joachim Hilgert and Tobias Weich},
journal= {arXiv preprint arXiv:1605.08801},
year = {2017}
}
Comments
Minor corrections. Added a discussion of the special case of an elementary convex co-compact group. To appear in Mathematische Annalen